Multiple scaling behavior and nonlinear traits in music scores

Abstract

We present a statistical analysis of music scores from different composers using detrended fluctuation analysis. We find different fluctuation profiles that correspond to distinct auto-correlation structures of the musical pieces. Further, we reveal evidence for the presence of nonlinear auto-correlations by estimating the detrended fluctuation analysis of the magnitude series, a result validated by a corresponding study of appropriate surrogate data. The amount and the character of nonlinear correlations vary from one composer to another. Finally, we performed a simple experiment in order to evaluate the pleasantness of the musical surrogate pieces in comparison with the original music and find that nonlinear correlations could play an important role in the aesthetic perception of a musical piece.